Can't speak for headphones, but in the 10 years I've been on head-fi, I've owned close to a 100 pairs of IEMs and never experienced a case of burn-in that I'd call significant.
I've heard very slight changes in sound signature of some dynamic drivers though, but only during the first few hours of playtime. I've never witnessed a change after the first 10 hours or so.
I'm fine with people who choose to believe in burn-in for themselves, but tbh, the way it's often advocated to others as a remedy for all kinds of shortcomings in IEMs makes me cringe. In my book the most convincing evidence that burn-in is largely expectation bias (wishful thinking) is the fact that 99.9% of listeners report a
change for the better. I'm pretty sure that if sound would really change significantly over time, some listeners would welcome that change and others wouldn't like it, so we'd end up with a more balanced statistics between
change for better and
change for worse.
Oh, and last not least, I've also managed to
kill one pair of IEMs by following a fellow member's recommendation to play it at high volume for 24 hours. So, if you really think you need to "burn" your IEMs, I'd recommend doing it at normal listening levels.